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A010030
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Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= [n/2]) = number of permutations of 1..n with [n/2]-k runs of consecutive pairs up and down (divided by 2).
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3
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1, 1, 0, 3, 0, 3, 8, 1, 25, 28, 7, 17, 155, 143, 45, 259, 1005, 933, 323, 131, 2770, 7488, 7150, 2621, 3177, 27978, 64164, 62310, 23811, 1281, 51433, 294602, 619986, 607445, 239653
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OFFSET
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1,4
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264.
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LINKS
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FORMULA
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G.f. for number of permutations of 1..n by number of runs of consecutive pairs up and down is Sum(n!*(((1-y)*(2*x^2-x^3)-x)/((1-y)*x^2-1))^n,n = 0 .. infinity), cf. A010029. - Vladeta Jovovic, Nov 23 2007
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EXAMPLE
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Triangle begins:
1,
1, 0,
3, 0,
3, 8, 1,
25, 28, 7,
17, 155, 143, 45,
259, 1005, 933, 323,
131, 2770, 7488, 7150, 2621,
3177, 27978, 64164, 62310, 23811,
1281, 51433, 294602, 619986, 607445, 239653,
...
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CROSSREFS
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KEYWORD
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tabf,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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